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September 3rd, 2015, 08:30 AM   #1
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Magnetic fields

Three endless wires are positioned as shown in the picture. The middle wire has two times smaller current. The distance of neighboring wires is a. Find all points on dotted lines in which the magnetic field is equal to 0.

Here's my try:

Magnetic fields created by the wires (in order from left to right):

$\displaystyle B_1=\frac{μ_o2I}{2πr_1}$

$\displaystyle B_2=\frac{μ_oI}{2πr_2}$

$\displaystyle B_3=\frac{μ_o2I}{2πr_3}$

$\displaystyle \vec B = \vec B_1+\vec B_2+\vec B_3$

$\displaystyle B_1+B_3=B_2$

$\displaystyle \frac{2}{r_1}+\frac{2}{r_3}=\frac{1}{r_2}$

$\displaystyle \frac{r_1r_3}{2r_3+2r_1}=r_2$

Last edited by kaspis245; September 3rd, 2015 at 08:41 AM.
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September 3rd, 2015, 09:15 AM   #2
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Math Focus: Wibbly wobbly timey-wimey stuff.
So far so good. If we consider a point on, say, the horizontal line, then assuming r1 is between wires 1 and 2 we get that r2 = a - r1, and r3 = r2 + a = 2a - r1.

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September 4th, 2015, 08:40 AM   #3
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Thanks, I did solve it.
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